Abstract
In this study, we establish exact solutions of fractional Kawahara equation by using the idea of exp ,left( { - varphi left( eta right)} right)-expansion method. The results of different studies show that the method is very effective and can be used as an alternative for finding exact solutions of nonlinear evolution equations (NLEEs) in mathematical physics. The solitary wave solutions are expressed by the hyperbolic, trigonometric, exponential and rational functions. Graphical representations along with the numerical data reinforce the efficacy of the used procedure. The specified idea is very effective, expedient for fractional PDEs, and could be extended to other physical problems.
Highlights
Most of the scientific problems and phenomena arise nonlinearly in various fields of mathematical physics and applied sciences, such as fluid mechanics, plasma physics, optical fibers, solid-state physics, and geochemistry
We have explained the different types of solitary wave solutions by setting the physical parameters as special values
Numerical discussion We have obtained the exact solutions (29), (30) and (31) in the above study and to know the correctness we have matched those solutions with the exact solution (Bongsoo 2009).We note that the absolute errors given in the tables from the solutions we have obtained are very precise and accurate
Summary
Most of the scientific problems and phenomena arise nonlinearly in various fields of mathematical physics and applied sciences, such as fluid mechanics, plasma physics, optical fibers, solid-state physics, and geochemistry. The investigation of travelling wave solutions (Shawagfeh 2002; Ray and Bera 2005; Yildirim et al 2011; Kilbas et al 2006; He and Li 2010; Momani and Al-Khaled 2005; Odibat and Momani 2007; Abdou 2007; Nassar et al 2011; Misirli and Gurefe 2011; Noor et al 2008; Ozis and Koroglu 2008; Wu and He 2007; Yusufoglu 2008; Zhang 2007; Zhu 2007; Wang et al 2008; Zayed et al 2004; Sirendaoreji 2004; Ali 2011; Liang et al 2011; He et al 2012; Jawad et al 2010; Zhou et al 2003; Yıldırım and Kocak 2009; Elbeleze et al 2013; Matinfar and Saeidy 2010; Ahmad 2014; Bongsoo 2009; Demiray and Pandir 2014, 2015; Lu 2012; Zayed and Amer 2014) of nonlinear evolution equations plays a significant role to look into the internal mechanism of nonlinear physical phenomena. Definition 4 The (left sided) Caputo partial fractional derivative of f with respect to t, f ∈ C−m1, m ∈ N ∪ {0}, is defined as: Dtμf (x, t)
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